Abstract
In this article, we discuss a least-squares/fictitious domain method for incompressible viscous flow around obstacles with Navier slip boundary condition. Assuming that Ω and B are two bounded sub-domains of Rd, with B‾⊂Ω, in order to solve the incompressible Navier–Stokes equations with a Navier slip condition on the boundary γ of the obstacle B, we advocate a fictitious domain method where one solves a simpler variant of the original problem on the whole Ω, followed by a well-chosen correction over B. This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. A detailed discussion of the finite element implementation of the above methodology is also provided. Numerical results are given; they suggest optimal order of convergence.
Original language | English |
---|---|
Pages (from-to) | 281-297 |
Number of pages | 17 |
Journal | Journal of Computational Physics |
Volume | 366 |
DOIs | |
Publication status | Published - 1 Aug 2018 |
Scopus Subject Areas
- Numerical Analysis
- Modelling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- Fictitious domain method
- Incompressible viscous flow
- Least-squares
- Navier slip boundary condition